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Analytical expressions for polar magnetoptics in magnetic multilayers

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Czechoslovak Journal of Physics Aims and scope

Abstract

This paper is a comprehensive study of different formalisms used to simulate polar magneto-optical (MO) effects in multilayers. A development of the 4 × 4 matrix calculation to first order in off-diagonal elements of the permittivity tensor gives original analytical expressions. They allow to express the MO effects in multilayers as a sum of contributions from individual layers. Each contribution consists of two components assigned to the interface and propagation effects. The explicit expressions for multilayers containing up to seven layers, together with those obtained in the frame of an ultrathin layer approximation, are shown to be useful both in a qualitative comprehension and in quantitative simulations of the experimental MO Kerr spectra of a wide variety of ultrathin magnetic structures. They can be used to separate the different contributions arising from the interfaces due to intermixing or spin polarization (including interface roughness) as well as to simulate magnetically coupled multilayers. As an example, the analytical expression is provided for a system consisting of two ultrathin films separated by a non-magnetic spacer and deposited on a non-magnetic substrate. The capabilities of the analytical expressions are demonstrated on MO spectroscopy in a broad spectral range of some well characterized ultrathin magnetic structures.

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Author information

Authors and Affiliations

  1. Institute of Physics, Charles University of Prague, Ke Karlovu 5, CZ-12116, Praha 2, Czech Republic

    Š. Višňovský, R. Lopušník, M. Nývlt & V. Prosser

  2. Laboratoire de Physique des Solides, UMR CNRS 2, Université Paris XI, 91405, Orsay, France

    J. Ferré

  3. Institut d’Electronique Fondamentale, UMR CNRS 8622, Université Paris XI, 91405, Orsay, France

    C. Train & P. Beauvillain

  4. Institut d’Optique Théorique et Appliquée, UMR CNRS 8501, Université Paris XI, 91405, Orsay, France

    D. Renard

  5. Laboratorie de Magnétisme et d’Optique, Université de Versailles, Bátiment Fermat, URA CNRS 1531, 45 Avenue des Etats-Unis, 78035, Versailles Cedex, France

    Š. Višňovský & R. Krishnan

  6. Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, UK

    J. A. C. Bland

Authors
  1. Š. Višňovský
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  2. R. Lopušník
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  3. M. Nývlt
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  4. V. Prosser
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  5. J. Ferré
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  6. C. Train
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  7. P. Beauvillain
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  8. D. Renard
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  9. R. Krishnan
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  10. J. A. C. Bland
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Additional information

This work has been partially supported by HCM programme “Magnetic properties of novel ultrathin films” (project number ERBCIPDCT940622), NATO Grant “High Technology” (LG931415) and Grant Agency of Czech Republic (# 202/97/1180 and # 202/00/0761).

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Višňovský, Š., Lopušník, R., Nývlt, M. et al. Analytical expressions for polar magnetoptics in magnetic multilayers. Czech J Phys 50, 857–882 (2000). https://doi.org/10.1023/A:1021482515115

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  • DOI: https://doi.org/10.1023/A:1021482515115

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